An Introduction to Holomorphic Dynamics
Spring 2019, TuTh 1:00-2:20
Physics P116

Instructor:    Araceli Bonifant  
Office: Math Tower 5D 148C
Phone: 632-8257

Office Hours: Monday 2:00-3:30 PM, Wednesday 2:00-3:30 PM and by appointment

Textbook: There is not required textbook. We will be using the notes of Professor Lasse Rempe-Gillen, who taught a similar class at the Department of Mathematical Science in Liverpool University. (I will provide copies of the Notes when the semester starts.)

Here are some further reading materials:

R. Devaney: An Introduction to Chaotic Dynamical Systems, 2nd Edition

J. Milnor: Dynamics in One Complex Variable, 3rd Edition (More advanced)

About the course: In this course we will explore the field of Complex Dynamics at an undergraduate level while reviewing, reinforcing, and extending the ideas learned in a typical first course on complex analysis. Julia sets and the famous Mandelbrot set will be introduced and interesting properties of their boundaries will be described. Towards the end of the course we will read a paper describing that the exponential map is chaotic.

This seminar course is aimed primarily at third- and fourth-year students majoring in mathematics. I will start by giving a few initial lectures, but after two or three weeks, I will assign topics to students to present in class. Each student will have 30 minutes to present the material assigned to him +5 minutes or so for questions during the presentation. Each student will have to present twice during the semester (see course syllabus for details).

This course satisfies the University SPK requirement. Here is the link of the requirement. The course is also a requirement for students graduating with Honors.

Clicking here: Course Schedule you will get a detailed syllabus of the course. The syllabus may change a little bit according to the needs of the class.

Prerequisites or Co-requisites:  Complex Analysis MAT342. It would be nice if students took also topology and geometry (MAT364) but it is not a big problem if you hadn't taken it.

Grading:The grading will be based primarily on class participation (20%), the quality of the student's in-class presentations (50%), homework sets (30%). Not attending regularly will have a negative effect on the grade. Regular attendance is therefore required.

Reading: Zalcman's paper V to complement the presentations of Liuming Wang and Connor Stewart.

The exponential map is chaotic: An invitation to transcendental dynamics, to complement the presentations of Brandon, Mosher D., Alexander, Moshe S., and Hubert.

Homework: Homework problems will be posted here.

Due Thursday February 7, 2019 Homework I

Due Thursday March 7, 2019 Homework II

Due Thursday March 14, 2019 Homework III

Due Tuesday April 9th, 2019 Homework IV

Due Tuesday April 23th, 2019 Homework V

Due Thursday May 9th, 2019 Homework VI

SASC Statement.If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact the Student Accessibility Support Center, 128 ECC Building, (631) 632-6748, or at They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential. Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and the Student Accessibility Support Center. For procedures and information go to the following website: and search Fire Safety and Evacuation and Disabilities.

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